306J of heat is required to raise the temperature of 2 moles of an ideal gas at constant pressure from 25°C to 35°C. The amount of heat required to raise the temperature of the same gas through the same range at constant volume is
(c) Given, at constant pressure heat Qp‌‌=306J ‌ Number of mole, ‌n‌‌=2 ∆T‌‌=T2−T1 ‌‌=35−25=10∘C We know that, Qp=nCp∆T ⇒‌306=2Cp×10 ⇒‌Cp=‌
306
2×10
⇒‌Cp=15.3J∕molK According to Mayer's formula, ⇒‌Cp−CV‌‌=R ⇒‌CV‌‌=Cp−R=15.3−8.314 ⇒‌CV‌‌=6.986J∕molK The amount of heat required to raise the temperature of gas at constant volume through same range of temperature. QV‌‌=nCV∆T ‌‌=2×6.986×(35−25) ‌‌=2×6.986×10 ‌‌=139.72∼eq140J