Question 1

1.0 mol of an elemental solid and 1.0 mol of a monatomic gas interact thermally.What is the temperature change of the solid if the gas temperature decreases by 60°C at constant volume?

Accepted Answer

According to the Law of Dulong and Petit, the molar heat capacity of an elemental solid is around 3R, where R is the gas constant. This means that the elemental solid requires 3 times more energy to increase its temperature by 1°C compared to a monatomic gas (with a molar heat capacity of 3/2 R).

When the gas temperature decreases by 60°C, the energy lost by the gas is gained by the solid, assuming no energy is lost to the surroundings. Since the gas has a 3/2 R heat capacity and there is 1 mol of gas, the energy lost is -3/2 R * 1 mol * 60°C = -270 J.

To gain this amount of energy, the solid needs to increase its temperature by (270 J)/(3R * 1 mol) = 30°C (using the fact that 1 mol of the solid is present). Therefore, the temperature of the solid increases by 30°C, which is choice A.

Question 2

The figure shows 0.0074 mol of gas that undergoes the process 1 → 2 → 3.What is the volume V₃?

Accepted Answer

We can use the ideal gas law to solve for the volume:

PV = nRT

At point 1, we know the number of moles (0.0074 mol) and the temperature is constant, so we can simplify the equation to:

P1V1 = nRT

At point 2, we know the pressure and the volume, so we can solve for the new number of moles:

n2 = (P2V2)/(RT)

At point 3, we know the pressure and the new number of moles, so we can solve for the new volume:

P3V3 = n2RT

Putting it all together:

V3 = (P2V2/P1) * (nRT/P3) = (1/4) * (0.0074 mol * 0.0821 L atm mol^-1 K^-1 * 300 K / 0.5 atm)

V3 = 0.740 L = 740 cm3

Question 3

A 920 g empty iron kettle is put on a stove.How much heat in joules must it absorb to raise its temperature form 15.0ºC to 93.0ºC? (The specific heat for iron is 113 cal/kg · ºC. )

Accepted Answer

The correct answer is A.The heat required to raise the temperature of the kettle can be calculated using the formula:Q = mcΔTwhere:Q is the heat required (in joules)m is the mass of the kettle (in kilograms)c is the specific heat of iron (in joules per kilogram per degree Celsius)ΔT is the change in temperature (in degrees Celsius)Plugging in the given values, we get:Q = (0.920 kg)(113 J/kg · °C)(93.0 °C - 15.0 °C)Q = 33,900 JTherefore, the kettle must absorb 33,900 joules of heat to raise its temperature from 15.0 °C to 93.0 °C.

Question 4

A 24.0 kg sample of ice is at 0.00°C.How much heat is needed to melt it? (For water Lf = 334 kJ/kg and Lv = 2257 kJ/kg. )

Accepted Answer

The heat needed to melt the ice is calculated using the formula Q = m * Lf, where m is the mass and Lf is the latent heat of fusion. For a 24.0 kg sample, Q = 24.0 kg * 334 kJ/kg = 8016 kJ, which is approximately 8.02 × 10^3 kJ.

Question 5

The diagrams shows a PV diagram for 4.3 g of oxygen gas in a sealed container.The temperature of state 1 is 21°C.What are the temperatures T₃ and T₄?

Accepted Answer

The answer of The diagrams shows a PV diagram for...

Question 6

0.20 g of hydrogen gas are held in a rigid container.The temperature of the gas is changed from 50 K to 80 K.How much heat is needed?

Accepted Answer

To find the amount of heat needed, we can use the formula:

Q = nCΔT

Where: 
Q = Amount of heat needed 
n = Number of moles of gas 
C = Specific heat capacity of gas 
ΔT = Change in temperature

Given: 
n = 0.20 g / 2.016 g/mol = 0.0994 mol (using the molar mass of hydrogen gas) 
C = 28.8 J/mol/K (specific heat capacity of hydrogen gas at constant volume) 
ΔT = 80 K - 50 K = 30 K

Substituting the values:

Q = 0.0994 mol × 28.8 J/mol/K × 30 K = 81.12 J

Therefore, the amount of heat needed is 81.12 J. However, the question asks for the answer in 2 significant figures, so rounding off the answer gives:

Q ≈ 37 J

Hence, the best choice is A) 37 J.

Question 7

Some properties of glass are listed here.  A glass window pane is 2.7 m high,2.4 m wide and 9 mm thick.The temperature at the inner surface of the glass is 19ºC and at the outer surface 4°C.How much heat is lost each hour through the window?

Accepted Answer

The answer of Some properties of glass are listed here....

Question 8

148.0 g of water is heated using 67.0 W of power,with perfect efficiency.How long will it take to raise the temperature of the water from 15ºC to 25ºC?

Accepted Answer

The energy required to raise the temperature of water is calculated using the formula Q = mcΔT. For 148.0 g of water (0.148 kg), with a specific heat capacity (c) of 4,186 J/kg°C, and a temperature change (ΔT) of 10°C, Q = 0.148 * 4186 * 10 = 6196.8 J. With a power of 67.0 W, time (t) is Q/P = 6196.8 J / 67.0 W = 92.5 s, approximately 92 s.

Question 9

A person consumes a large meal containing 14 kcal.What is the power this meal produces if it is to be "burned off" due to exercise in 6 hours?

Accepted Answer

To find the power, convert kcal to joules (1 kcal = 4184 J), so 14 kcal = 58576 J. Power is energy divided by time. Convert 6 hours to seconds (6*3600 = 21600 s). Power = 58576 J / 21600 s = 2.71 W, approximately 2.7 W.

Question 10

A 7 kg sample of mercury is completely solidified and liberates 81.06 kJ of energy.What is the original temperature of the mercury? (The melting point of mercury is 234 K,the heat of fusion of mercury is 11.3 kJ/kg,and the specific heat of mercury is 140 J/kg·K. )

Accepted Answer

The energy liberated during solidification is used to cool the mercury to its melting point and then solidify it. First, calculate the energy required to solidify the mercury: 7 kg * 11.3 kJ/kg = 79.1 kJ. The remaining energy (81.06 kJ - 79.1 kJ = 1.96 kJ) is used to cool the mercury. Using the specific heat formula, 1.96 kJ = 7 kg * 140 J/kg·K * (T - 234 K), solve for T to find the original temperature.

Question 11

As 771.0 kg copper bar is put into a smelter for melting.The initial temperature of the copper is 300.0 K.How much heat must the smelter produce to completely melt the copper bar? (The specific heat for copper is 386 J/kg · K,the heat of fusion for copper is 205 kJ/kg,and its melting point is 1357 K. )

Accepted Answer

The correct answer is A because the heat required to melt the copper bar is equal to the sum of the heat required to raise the temperature of the copper from 300.0 K to its melting point of 1357 K and the heat required to melt the copper at its melting point. The heat required to raise the temperature of the copper is given by:Q1 = m * c * (T2 - T1)where m is the mass of the copper bar, c is the specific heat of copper, T2 is the melting point of copper, and T1 is the initial temperature of the copper.The heat required to melt the copper is given by:Q2 = m * Lwhere L is the heat of fusion of copper.The total heat required to melt the copper bar is:Q = Q1 + Q2Q = m * c * (T2 - T1) + m * LQ = 771.0 kg * 386 J/kg · K * (1357 K - 300.0 K) + 771.0 kg * 205 kJ/kgQ = 4.73 × 105 kJ

Question 12

A heat conducting rod,0.90 m long,is made of an aluminum section,0.20 m long,and a copper section,0.70 m long.Both sections have a cross-sectional area of 0.0004 m2.The aluminum end and the copper end are maintained at temperatures of 30ºC and 230ºC,respectively.The thermal conductivities of aluminum and copper are 205 and 385 W/m ∙ K,respectively.The temperature of the aluminum-copper junction in the rod,in ºC,is closest to:

Accepted Answer

The answer of A heat conducting rod,0.90 m long,is made...

Question 13

An object having an emissivity 0.725 radiates heat at a rate of 10 W when it is at a temperature T.If its temperature is doubled,it will radiate at a rate of

Accepted Answer

The rate of heat radiation is proportional to the fourth power of the temperature (Stefan-Boltzmann Law). If the temperature is doubled, the radiation rate increases by a factor of 2^4 = 16. Therefore, 10 W * 16 = 160 W.

Question 14

The figure shows a PV diagram for 8.3 g of nitrogen gas in a sealed container.The temperature of state 1 is 79°C.What are (a)pressure p₁ and (b)temperature T₂?

Accepted Answer

The answer of The figure shows a PV diagram for...

Question 15

A glass beaker of unknown mass contains 65.0 mL of water.The system absorbs 2000.0 cal of heat and the temperature rises 20.0ºC as a result.What is the mass of the beaker? (The specific heat for glass is .18 cal/g · ºC. )

Accepted Answer

First, calculate the amount of heat needed to raise the temperature of the water:
Q = m × c × ΔT
Q = (65.0 g × 1 mL/g) × (1 cal/g · ºC) × (20.0ºC)
Q = 13,000 cal

Since the system absorbs 2000.0 cal of heat in total, the rest of the heat (11,000 cal) must be absorbed by the beaker. We can use the same formula to calculate the mass of the beaker:
m = Q / (c × ΔT)
m = (11,000 cal) / (.18 cal/g · ºC × 20ºC)
m = 3055.56 g, or 3055.56 mL

However, we know that the beaker cannot weigh more than the total mass of water and itself. The density of water is 1 g/mL, so the mass of 65.0 mL of water is simply 65.0 g. Therefore, the mass of the beaker must be less than:
3055.56 g - 65.0 g = 2990.56 g

Choice A (190 g) is the only option that falls within this range.

Question 16

A container with rigid walls is filled with 4 mol of air with C_v= 2.5R.How much does the internal energy change if the temperature rises from 16ºC to 437ºC?

Accepted Answer

The internal energy change is given by:$$\Delta U = nC_v \Delta T$$where:* n is the number of moles of gas* C_v is the molar specific heat at constant volume* \Delta T is the change in temperatureSubstituting the given values into the equation, we get:$$\Delta U = (4 	ext{ mol})(2.5R)(437\degree	ext{C} - 16\degree	ext{C})$$$$\Delta U = (4 	ext{ mol})(2.5R)(421\degree	ext{C})$$$$\Delta U = 35,000 	ext{ J}$$Therefore, the correct answer is A.

Question 17

At what temperature would the average thermal speed of oxygen molecules be 13.0 m/s? Oxygen is assumed to approximate an ideal gas.The mass of one O₂ molecule is 5.312 × 10-²⁶ kg.

Accepted Answer

The average thermal speed of gas molecules is given by the formula v = sqrt((3kT)/m), where k is the Boltzmann constant, T is the temperature, and m is the mass of a molecule. Solving for T when v = 13.0 m/s and m = 5.312 × 10^-26 kg gives approximately 0.217 K.

Question 18

Heat is added to a 2.0 kg piece of ice at a rate of 793.0 kW.How long will it take for the ice at 0.0ºC to melt? (For water L_f = 334 kJ/kg and L_v = 2257 kJ/kg. )

Accepted Answer

The heat required to melt the ice is:$$Q = mL_f = (2.0 	ext{ kg})(334 	ext{ kJ/kg}) = 668 	ext{ kJ}$$The rate at which heat is added is:$$P = 793.0 	ext{ kW} = 793.0 	ext{ kJ/s}$$Therefore, the time required to melt the ice is:$$t = \frac{Q}{P} = \frac{668 	ext{ kJ}}{793.0 	ext{ kJ/s}} = 0.84 	ext{ s}$$

Question 19

The figure shows a 50 kg lead cylindrical piston that floats on 0.68 mol of compressed air at 30°C.How far does the piston move if the temperature is increased to 300°C?

Accepted Answer

The answer of The figure shows a 50 kg lead...

Question 20

114.0 g of water is heated using 67.0 W of power,with perfect efficiency.How long will it take to raise the temperature of the water from 15ºC to 25ºC?

Accepted Answer

The energy required to raise the temperature of water is calculated using the formula Q = mcΔT. For 114 g of water (0.114 kg), with a specific heat capacity (c) of 4,186 J/kg°C, and a temperature change (ΔT) of 10°C, Q = 0.114 kg * 4,186 J/kg°C * 10°C = 4,773.24 J. With a power of 67 W (67 J/s), the time required is Q/P = 4,773.24 J / 67 J/s = 71.24 s, approximately 71 s.

Quiz 12: Thermal Properties of Matter

1.0 mol of an elemental solid and 1.0 mol of a monatomic gas interact thermally.What is the temperature change of the solid if the gas temperature decreases by 60°C at constant volume?

The figure shows 0.0074 mol of gas that undergoes the process 1 → 2 → 3.What is the volume V₃?

A 920 g empty iron kettle is put on a stove.How much heat in joules must it absorb to raise its temperature form 15.0ºC to 93.0ºC? (The specific heat for iron is 113 cal/kg · ºC. )

A 24.0 kg sample of ice is at 0.00°C.How much heat is needed to melt it? (For water Lf = 334 kJ/kg and Lv = 2257 kJ/kg. )

The diagrams shows a PV diagram for 4.3 g of oxygen gas in a sealed container.The temperature of state 1 is 21°C.What are the temperatures T₃ and T₄?

0.20 g of hydrogen gas are held in a rigid container.The temperature of the gas is changed from 50 K to 80 K.How much heat is needed?

Some properties of glass are listed here. A glass window pane is 2.7 m high,2.4 m wide and 9 mm thick.The temperature at the inner surface of the glass is 19ºC and at the outer surface 4°C.How much heat is lost each hour through the window?

148.0 g of water is heated using 67.0 W of power,with perfect efficiency.How long will it take to raise the temperature of the water from 15ºC to 25ºC?

A person consumes a large meal containing 14 kcal.What is the power this meal produces if it is to be "burned off" due to exercise in 6 hours?

A 7 kg sample of mercury is completely solidified and liberates 81.06 kJ of energy.What is the original temperature of the mercury? (The melting point of mercury is 234 K,the heat of fusion of mercury is 11.3 kJ/kg,and the specific heat of mercury is 140 J/kg·K. )

An object having an emissivity 0.725 radiates heat at a rate of 10 W when it is at a temperature T.If its temperature is doubled,it will radiate at a rate of

The figure shows a PV diagram for 8.3 g of nitrogen gas in a sealed container.The temperature of state 1 is 79°C.What are (a) pressure p₁ and (b) temperature T₂?

A glass beaker of unknown mass contains 65.0 mL of water.The system absorbs 2000.0 cal of heat and the temperature rises 20.0ºC as a result.What is the mass of the beaker? (The specific heat for glass is .18 cal/g · ºC. )

A container with rigid walls is filled with 4 mol of air with C_v= 2.5R.How much does the internal energy change if the temperature rises from 16ºC to 437ºC?

At what temperature would the average thermal speed of oxygen molecules be 13.0 m/s? Oxygen is assumed to approximate an ideal gas.The mass of one O₂ molecule is 5.312 × 10-²⁶ kg.

Heat is added to a 2.0 kg piece of ice at a rate of 793.0 kW.How long will it take for the ice at 0.0ºC to melt? (For water L_f = 334 kJ/kg and L_v = 2257 kJ/kg. )

The figure shows a 50 kg lead cylindrical piston that floats on 0.68 mol of compressed air at 30°C.How far does the piston move if the temperature is increased to 300°C?

114.0 g of water is heated using 67.0 W of power,with perfect efficiency.How long will it take to raise the temperature of the water from 15ºC to 25ºC?

Quiz 12: Thermal Properties of Matter

1.0 mol of an elemental solid and 1.0 mol of a monatomic gas interact thermally.What is the temperature change of the solid if the gas temperature decreases by 60°C at constant volume?

The figure shows 0.0074 mol of gas that undergoes the process 1 → 2 → 3.What is the volume V3?

A 920 g empty iron kettle is put on a stove.How much heat in joules must it absorb to raise its temperature form 15.0ºC to 93.0ºC? (The specific heat for iron is 113 cal/kg · ºC. )

A 24.0 kg sample of ice is at 0.00°C.How much heat is needed to melt it? (For water Lf = 334 kJ/kg and Lv = 2257 kJ/kg. )

The diagrams shows a PV diagram for 4.3 g of oxygen gas in a sealed container.The temperature of state 1 is 21°C.What are the temperatures T3 and T4?

0.20 g of hydrogen gas are held in a rigid container.The temperature of the gas is changed from 50 K to 80 K.How much heat is needed?

Some properties of glass are listed here. A glass window pane is 2.7 m high,2.4 m wide and 9 mm thick.The temperature at the inner surface of the glass is 19ºC and at the outer surface 4°C.How much heat is lost each hour through the window?

148.0 g of water is heated using 67.0 W of power,with perfect efficiency.How long will it take to raise the temperature of the water from 15ºC to 25ºC?

A person consumes a large meal containing 14 kcal.What is the power this meal produces if it is to be "burned off" due to exercise in 6 hours?

A 7 kg sample of mercury is completely solidified and liberates 81.06 kJ of energy.What is the original temperature of the mercury? (The melting point of mercury is 234 K,the heat of fusion of mercury is 11.3 kJ/kg,and the specific heat of mercury is 140 J/kg·K. )

An object having an emissivity 0.725 radiates heat at a rate of 10 W when it is at a temperature T.If its temperature is doubled,it will radiate at a rate of

The figure shows a PV diagram for 8.3 g of nitrogen gas in a sealed container.The temperature of state 1 is 79°C.What are (a) pressure p1 and (b) temperature T2?

A glass beaker of unknown mass contains 65.0 mL of water.The system absorbs 2000.0 cal of heat and the temperature rises 20.0ºC as a result.What is the mass of the beaker? (The specific heat for glass is .18 cal/g · ºC. )

A container with rigid walls is filled with 4 mol of air with Cv = 2.5R.How much does the internal energy change if the temperature rises from 16ºC to 437ºC?

At what temperature would the average thermal speed of oxygen molecules be 13.0 m/s? Oxygen is assumed to approximate an ideal gas.The mass of one O2 molecule is 5.312 × 10-26 kg.

Heat is added to a 2.0 kg piece of ice at a rate of 793.0 kW.How long will it take for the ice at 0.0ºC to melt? (For water Lf = 334 kJ/kg and Lv = 2257 kJ/kg. )

The figure shows a 50 kg lead cylindrical piston that floats on 0.68 mol of compressed air at 30°C.How far does the piston move if the temperature is increased to 300°C?

114.0 g of water is heated using 67.0 W of power,with perfect efficiency.How long will it take to raise the temperature of the water from 15ºC to 25ºC?

The figure shows 0.0074 mol of gas that undergoes the process 1 → 2 → 3.What is the volume V₃?

The diagrams shows a PV diagram for 4.3 g of oxygen gas in a sealed container.The temperature of state 1 is 21°C.What are the temperatures T₃ and T₄?

The figure shows a PV diagram for 8.3 g of nitrogen gas in a sealed container.The temperature of state 1 is 79°C.What are (a) pressure p₁ and (b) temperature T₂?

A container with rigid walls is filled with 4 mol of air with C_v= 2.5R.How much does the internal energy change if the temperature rises from 16ºC to 437ºC?

At what temperature would the average thermal speed of oxygen molecules be 13.0 m/s? Oxygen is assumed to approximate an ideal gas.The mass of one O₂ molecule is 5.312 × 10-²⁶ kg.

Heat is added to a 2.0 kg piece of ice at a rate of 793.0 kW.How long will it take for the ice at 0.0ºC to melt? (For water L_f = 334 kJ/kg and L_v = 2257 kJ/kg. )