Answer to Question #146070 in Physics for Khan Asf

Question

An ideal gas in the amount of 0, 9 moles first expands isobarrically and then cools isochorically. During the entire process, an amount of heat 2000 J is transferred to the gas. The initial and final gas temperatures are the same and equal to 260 K. Find the ratio of the final gas volume to its initial volume.

Answer 1

After the isochoric cooling, the temperature is 260 K, the heat transferred to the gas is 0 (no work done and it is cooling). During the process of isobaric expansion the heat transferred is

$$Q=P\Delta V=PV_2-PV_1.\\ PV_1=nRT_1,\\ PV_2=nRT_2.\\\space\\ Q=nRT_2-nRT_1,\\\space\\ T_2=\frac{Q}{nR}+T_1.$$

From the first process of isobaric expansion, we have

$$\frac{V_2}{V_1}=\frac{T_2}{T_1},\\\space\\ \frac{V_2}{V_1}=\frac{Q}{nRT_1}+1=2.03.$$