We start with 5.00 moles of an ideal monatomic gas with an initial temperature of 129 degrees Celcius. The gas expands and, in the process, absorbs an amount of heat equal to 1240 J and does an amount of work equal to 2120 J.
What is the final temperature, T_final, of the gas?
Use R = 8.3145 J/(mol.K) for the ideal gas constant.
absorbing an amount of heat of 1240 J and doing an amount of work of 2120 J, would left an internal energy change of:
1240J – 2120J = -880J
for this 5.00 moles of gas, or -176J/mol
For monatomic gas, there are three translational degrees of freedom, and thus its thermal capacity is: 3R/2 = 12.4718J/mol∙K. Thus the final temperature, T_final, of the gas is:
T_final = 129 – 176/12.4718 = 115 (degrees Celcius)