70 calories of heat are required to raise the temperature of 2 moles of an ideal gas at constant pressure from 30°C to 35°C.The amount of heat required to raise the temperature of the same sample of the gas through the same range at constant volume is (Gas constant = 1.99 cal/K-mole)

Question

70 calories of heat are required to raise the temperature of 2 moles of an ideal gas at constant pressure from 30°C to 35°C.The amount of heat required to raise the temperature of the same sample of the gas through the same range at constant volume is (Gas constant = 1.99 cal/K-mole) (A) 30 cal (B) 50 cal (C) 70 cal (D) 90 cal

Tardigrade Admin · Accepted Answer

As dQ = CPmΔT ⇒ 70 = CP ×; 2(35 - 30) ⇒ CP = 7 cal/mole/°C CV = CP - R = 7 - 1.99 = 5.01 cal mol-1 °C-1 ∴ dQ' = CVmΔT = 5.01 × 2 × (35 - 30) = 50.1 cal

Q. 70 calories of heat are required to raise the temperature of 2 moles of an ideal gas at constant pressure from 30∘C to 35∘C.The amount of heat required to raise the temperature of the same sample of the gas through the same range at constant volume is (Gas constant = 1.99 cal/K-mole)

30 cal

50 cal

70 cal

90 cal

As dQ = CPmΔT \Rightarrow 70 = CP \times; 2(35 - 30) \Rightarrow CP = 7 cal/mole/∘C CV = CP - R = 7 - 1.99 = 5.01 cal mol-1 ∘C-1 ∴ dQ′ = CVmΔT = 5.01 × 2 × (35 - 30) = 50.1 cal

As dQ = C_Pm $Δ$ T
\Rightarrow 70 = C_P \times; 2(35 - 30)
\Rightarrow C_P = 7 cal/mole/ $^{\circ}$ C
C_V = C_P - R
= 7 - 1.99 = 5.01 cal mol^-1 $^{\circ}$ C^-1
∴ dQ $^{^{'}}$ = C_Vm $Δ$ T
= 5.01 $\times$ 2 $\times$ (35 - 30) = 50.1 cal