A cylinder contains 23 moles of an ideal gas at a temperature of 300 K.The gas is compressed at constant pressure until the final volume equals 0.43 times the initial volume.The molar heat capacity at constant volume of the gas is 24.0 J/mol • K and the ideal gas constant is R = 8.314 J/mol • K.The heat absorbed by the gas is closest to

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The heat absorbed by the gas is given by:$$Q = nC_v(T_f - T_i)$$where:* $n$ is the number of moles of gas* $C_v$ is the molar heat capacity at constant volume* $T_f$ is the final temperature* $T_i$ is the initial temperatureWe are given that $n = 23 	ext{ mol}$, $C_v = 24.0 	ext{ J/mol} \cdot 	ext{K}$, $T_i = 300 	ext{ K}$, and $V_f = 0.43V_i$. We can use the ideal gas law to find $T_f$:$$PV = nRT$$where:* $P$ is the pressure* $V$ is the volume* $R$ is the ideal gas constantSince the pressure is constant, we have:$$\frac{V_i}{T_i} = \frac{V_f}{T_f}$$Substituting $V_f = 0.43V_i$, we get:$$\frac{V_i}{T_i} = \frac{0.43V_i}{T_f}$$Solving for $T_f$, we get:$$T_f = \frac{T_i}{0.43} = \frac{300 	ext{ K}}{0.43} = 698 	ext{ K}$$Now we can calculate the heat absorbed by the gas:$$Q = nC_v(T_f - T_i) = (23 	ext{ mol})(24.0 	ext{ J/mol} \cdot 	ext{K})(698 	ext{ K} - 300 	ext{ K}) = -130 	ext{ kJ}$$Therefore, the heat absorbed by the gas is closest to -130 kJ.

A Cylinder Contains 23 Moles of an Ideal Gas at a Temperature