Forty calories of heat is needed to raise the temperature of 1 mol of an ideal monatomic gas from 20° C to 30° C at a constant pressure. The amount of heat required to raise its temperature over the same interval at a constant volume (R=2 cal mol -1 K -1) is

Question

Forty calories of heat is needed to raise the temperature of 1 mol of an ideal monatomic gas from 20° C to 30° C at a constant pressure. The amount of heat required to raise its temperature over the same interval at a constant volume (R=2 cal mol -1 K -1) is (A) 20 cal (B) 40 cal (C) 60 cal (D) 80 cal

Tardigrade Admin · Accepted Answer

At constant pressure Qp=μ Cp Δ T =1 × Cp ×(30-20)=40 cal ⇒ Cp=4 cal / mol - K ∴ Cv=Cp-R=4-2=2 cal / mol - K Now Qv=μ Cv Δ T=1 × 2 ×(30-20)=20 cal

Q. Forty calories of heat is needed to raise the temperature of $1 m o l$ of an ideal monatomic gas from $2 0^{\circ} C$ to $3 0^{\circ} C$ at a constant pressure. The amount of heat required to raise its temperature over the same interval at a constant volume $(R = 2 c a l m o l^{- 1} K^{- 1})$ is

$20 c a l$

$40 c a l$

$60 c a l$

$80 c a l$

At constant pressure $Q_{p} = μ C_{p} Δ T$
$= 1 \times C_{p} \times (30 - 20) = 40 c a l$
$\Rightarrow C_{p} = 4 c a l / m o l - K$
$∴ C_{v} = C_{p} - R = 4 - 2 = 2 c a l / m o l - K$
Now $Q_{v} = μ C_{v} Δ T = 1 \times 2 \times (30 - 20) = 20 c a l$

Q. Forty calories of heat is needed to raise the temperature of 1mol of an ideal monatomic gas from 20∘C to 30∘C at a constant pressure. The amount of heat required to raise its temperature over the same interval at a constant volume (R=2calmol−1K−1) is

20cal

40cal

60cal

80cal