Problem 2

One mole of a monatomic ideal gas initially at

(P_0,V_0,T_0)

is heated at constant pressure until its volume is

2V_0

. Find the final temperature, work done by the gas, heat absorbed, and change in internal energy. Use the gas constant

R

. (a) State the assumptions and establish the governing equation for the requested quantity. (b) Solve it in terms of the given symbols, identifying the direction, sign, or physical nature of the result. (c) Check a simple limiting case and state when the model remains valid. Use SI units consistently, retain the symbols in the setup, and enforce all geometric constraints and initial conditions.

problems.proof.stepOf

problems.proof.prevStep problems.proof.nextStep

\Delta U=\frac32R(T_f-T_0)=\frac32RT_0

problems.proof.analysis

For one mole of a monatomic gas, $U=3RT/2$ ; internal energy depends only on temperature.