Question

310 J of heat is required to raise the temperature of 2 mol of an ideal gas at constant pressure from 25 degree celsius to 35 degree celsius. The amount of heat required to raise the temperature of the gas through the same range at constant volume is a. 384 J b. 144 J c. 276 J d. 452 J

Answer 1

Given :

➳ Heat required to raised temp. from 25°C to 35°C = 310J (at constant pressure)

➳ Moles of gas = 2

To Find :

➨ Heat required to raise the temperature of the gas through the same range at constant volume.

SoluTion :

✴ Process at constant Pressure :

⇒ Q = n × Cp × ΔT

⇒ 310 = 2 × Cp × (35 - 25)

⇒ 310 = 20Cp

⇒ Cp = 15.5 J/mol K

✴ Relation b/w Cp and Cv :

➢ Cp - Cv = R

➢ 15.5 - Cv = 8.314

➢ Cv = 15.5 - 8.314

➢ Cv = 7.186 J/mol K

✴ Process at constant Volume :

➠ Q = n × Cv × ΔT

➠ Q = 2 × 7.186 × (35 - 25)

➠ Q = 14.4 × 10

➠ Q = 144J