One mole of an ideal gas requires 207 J heat to rise the temperature by 10 K when heated at constant pressure. If the same gas is heated at constant volume to raise the temperature by the same 10 K, the heat required is (Given the gas constant R = 8.3 J/mole K)

Question

One mole of an ideal gas requires 207 J heat to rise the temperature by 10 K when heated at constant pressure. If the same gas is heated at constant volume to raise the temperature by the same 10 K, the heat required is (Given the gas constant R = 8.3 J/mole K) (A) 198.7 J (B) 29 J (C) 215.3 J (D) 124 J

Tardigrade Admin · Accepted Answer

Using CP-CV=R, CP is heat needed for raising by 10 K. ∴ CP=20.7 J/mole K Given R = 8.3 J/mole K ∴ CV=20.7-8.3=12.4 J/mole K ∴ For raising by 10 K. = 124 J.

Q. One mole of an ideal gas requires 207 J heat to
rise the temperature by 10 K when heated at
constant pressure. If the same gas is heated at
constant volume to raise the temperature by the
same 10 K, the heat required is
(Given the gas constant R = 8.3 J/mole K)

198.7 J

29 J

215.3 J

124 J

Using $C_{P} - C_{V} = R,$
$C_{P}$ is heat needed for raising by 10 K.
$∴ C_{P} = 20.7 J / m o l e K$
Given R = 8.3 J/mole K
$∴ C_{V} = 20.7 - 8.3 = 12.4 J / m o l e K$
$∴$ For raising by 10 K. = 124 J.

Q. One mole of an ideal gas requires 207 J heat to rise the temperature by 10 K when heated at constant pressure. If the same gas is heated at constant volume to raise the temperature by the same 10 K, the heat required is (Given the gas constant R = 8.3 J/mole K)