One mole of ideal monatomic gas follows V=aT² from T₀ to 2T₀. If its molar heat capacity is (n/2)R, find n.
Physics · Mixed Chapter
JEE Main Practice

Question

One mole of ideal monatomic gas follows V=aT² from T₀ to 2T₀. If its molar heat capacity is (n/2)R, find n.

G1 Physics · Accepted Answer

Step 1: First law δQ=dU+PdV. For monatomic gas, dU=(3/2)R dT per mole. Step 2: V=aT² gives dV/V=2dT/T. From PV=RT, PdV=RT(dV/V)=2R dT. Step 3: δQ=[(3/2)+2]R dT=(7/2)R dT. Step 4: C=(7/2)R ⇒n=7.