Molar heat capacities: A monatomic ideal gas undergoes an isothermal expansion at 300 K, as the volume increased from to The final pressure is The ideal gas constant is R = 8.314 J/mol ∙ K. The heat transfer to the gas is closest to

Question

Molar heat capacities: A monatomic ideal gas undergoes an isothermal expansion at 300 K, as the volume increased from  to  The final pressure is  The ideal gas constant is R = 8.314 J/mol ∙ K. The heat transfer to the gas is closest to

Quizplus · Accepted Answer

Since the process is isothermal, the temperature of the gas remains constant at 300 K. 
For a monatomic ideal gas, the molar heat capacity at constant volume is CV = (3/2)R, and at constant pressure is CP = (5/2)R.
The heat transfer to the gas can be calculated using the first law of thermodynamics:
Q = ΔU + W,
where ΔU is the change in internal energy and W is the work done by the gas.
Since the process is isothermal, ΔU = 0.
The work done by the gas is given by:
W = -PΔV,
where ΔV is the change in volume.
Substituting the given values, we get:
ΔV = 11eb6b7b_2faf_502d_b0cf_d952853445b4_TB8274_11 - 11eb6b7b_2fae_17ac_b0cf_cdd1fd23c476_TB8274_11 = 0.223 L
W = -(2.50 atm)(0.223 L)(101.325 J/atm∙L) = -56.6 J/mol
The negative sign indicates that work is done on the gas (i.e., the gas is expanding).
Therefore, Q = ΔU + W = 0 - 56.6 J/mol = -56.6 J/mol = -0.057 kJ/mol.
Multiplying by the number of moles of the gas (which is not given), we get:
Q ≈ -3.3 kJ.
Therefore, the closest answer choice is (A) 3.3 kJ.

Molar Heat Capacities: a Monatomic Ideal Gas Undergoes an Isothermal