Problem 2

One mole of monatomic ideal gas in fixed volume

V

is heated from absolute temperature

T_1

T_2>T_1

. Take

W>0

as work done by the gas, neglect macroscopic kinetic and potential energy changes, and use gas constant

R

. (a) Find initial and final pressure. (b) Find work, internal-energy change, and heat supplied. (c) Explain the heat sign and how pressure changes. Keep the sign convention consistent and use appropriate SI units throughout. Each part builds on intermediate results from the preceding part; apply a physical relation only where the stated model assumptions hold. Finally compare the answers with the initial conditions, expected trends, and an independent check when available.

problems.proof.stepOf

problems.proof.prevStep problems.proof.nextStep

\boxed{p_1=RT_1/V,\quad p_2=RT_2/V,\quad W=0,\quad Q=\Delta U=\frac32R(T_2-T_1)}

problems.proof.analysis

Collect answers to every part, including signs, directions, and image or process properties where relevant. Dimensions match the physical quantities.