For the same rise in temperature of one mole of gas at constant volume, the heat required for a non-linear triatomic gas is K times that required for monatomic gas. The value of K is

Question

For the same rise in temperature of one mole of gas at constant volume, the heat required for a non-linear triatomic gas is K times that required for monatomic gas. The value of K is (A) 1 (B) 0.5 (C) 2 (D) 2.5

Tardigrade Admin · Accepted Answer

For a non-linear triatomic gas, Cv=3R And for a monoatomic gas, Cv â²=(3/2)R ∴ (Q/Qâ²)=(Cv/Cv â²)=K=(3 R/(3)2 R)=2

Q. For the same rise in temperature of one mole of gas at constant volume, the heat required for a non-linear triatomic gas is $K$ times that required for monatomic gas. The value of $K$ is

$1$

$0.5$

$2$

$2.5$

For a non-linear triatomic gas, $C_{v} = 3 R$
And for a monoatomic gas, $C_{v}' = \frac{3}{2} R$
$∴ \frac{Q}{Q ^{'}} = \frac{C _{v}}{C _{v} '} = K = \frac{3 R}{\frac{3}{2} R} = 2$

Q. For the same rise in temperature of one mole of gas at constant volume, the heat required for a non-linear triatomic gas is K times that required for monatomic gas. The value of K is

1

0.5

2

2.5

For a non-linear triatomic gas, Cv​=3R And for a monoatomic gas, Cv​′=23​R ∴Q′Q​=Cv​′Cv​​=K=23​R3R​=2

Q. For the same rise in temperature of one mole of gas at constant volume, the heat required for a non-linear triatomic gas is $K$ times that required for monatomic gas. The value of $K$ is

$1$

$0.5$

$2$

$2.5$

For a non-linear triatomic gas, $C_{v} = 3 R$
And for a monoatomic gas, $C_{v}' = \frac{3}{2} R$
$∴ \frac{Q}{Q ^{'}} = \frac{C _{v}}{C _{v} '} = K = \frac{3 R}{\frac{3}{2} R} = 2$