Question

70 calories of heat are required to raise the temperature of 2 mole 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 gas through the same range at constant volume is

विकल्प

• 30 calories

• 50 calories

• 70 calories

• 90 calories

Answer 1

50 calories
It is given that 70 calories of heat are required to raise the temperature of 2 mole of an ideal gas at constant pressure from 30° C to 35° C. Also, specific heat at constant pressure,

`"C"_"P" = (triangle Q)/(ntriangleT)`

`=> "C"_"P" = 70/ (2 xx (35-30)`

`=> "C"_"P" =70/(2 xx 5)`

`=> "C"_"P" = 7 "calories" -" mol" ^-1K^-1`

For an ideal gas , 

C_P - C_V = R = 8.314 J - mol ^-1 K^-1 ≃ 2 calories mol^-1K^-1 

⇒ C_V =C_P -R

⇒ C_V = (7-2) calories - mol^-1 K^-1

⇒ C_V = 5 calories - mol^-1 K^-1

⇒ C_V = `(triangle "Q")/(ntriangle"T")`

`=> 5 = (triangle "Q")/(2 xx (35-30)`

⇒ Δ Q = 5 × 2 × (35-30)

⇒ Δ Q = 5 × 2 × 5

⇒ Δ Q = 50 calories

Therefore, 50 calories need to be supplied to raise the temperature of 2 moles of gas from 30-35 ^oC at constant volume.