A sealed rigid tank contains 29 moles of an ideal gas, at an initial temperature of $270 \mathrm {~K}$ The pressure of the gas is increased until the final pressure equals 1.90 times the initial pressure. The heat capacity at constant pressure of the gas is $24.0 \mathrm {~J} / \mathrm { mol } \cdot \mathrm { K }$ How much heat is absorbed by the gas during this process? (R = 8.31 J/mol ? K)

Question

Quizplus · Accepted Answer

Explanation:The heat absorbed by the gas is given by:$$Q = nC_p(T_f - T_i)$$where:n is the number of moles of gas$C_p$ is the heat capacity at constant pressure$T_f$ is the final temperature$T_i$ is the initial temperatureSubstituting the given values into the equation, we get:$$Q = (29 \mathrm {~mol})(24.0 \mathrm {~J} / \mathrm { mol } \cdot \mathrm { K })(T_f - 270 \mathrm {~K})$$We can find $T_f$ using the ideal gas law:$$PV = nRT$$where:P is the pressureV is the volumeR is the ideal gas constantSince the volume is constant, we have:$$\frac{P_i}{T_i} = \frac{P_f}{T_f}$$Substituting the given values into the equation, we get:$$\frac{P_i}{270 \mathrm {~K}} = \frac{1.90P_i}{T_f}$$Solving for $T_f$, we get:$$T_f = 513 \mathrm {~K}$$Substituting this value into the equation for Q, we get:$$Q = (29 \mathrm {~mol})(24.0 \mathrm {~J} / \mathrm { mol } \cdot \mathrm { K })(513 \mathrm {~K} - 270 \mathrm {~K})$$$$Q = 110 \mathrm {~kJ}$$Therefore, the correct answer is A.

A Sealed Rigid Tank Contains 29 Moles of an Ideal 270 K270 \mathrm {~K}270 K

A Sealed Rigid Tank Contains 29 Moles of an Ideal $270 \mathrm {~K}$