# Physics Heat transfer question (will award BEST ANSWER)?

Physics Heat transfer question (will award BEST ANSWER)?

• A

Process A is a constant volume process. The heat transferred in such a process equals the change in internal energy of the gas.

Q = ∆U

Assuming ideal gas behavior the change in internal energy of the nitrogen gas is given by:

∆U = n∙Cv∙∆T

The molar heat capacity at constant volume for an diatomic ideal gas like nitrogen is

Cv = (5/2)∙R

Hence,

Q =∙(5/2)∙n∙R∙∆T

From ideal gas law

n∙R∙T = p∙V

follows for an constant volume process:

n∙R∙∆T = ∆(p∙V) = V∙∆p

Hence,

Q =∙(5/2)∙V∙∆p = (5/2)∙V∙(p_f – p_i)

= (5/2) ∙ 2000cm³ ∙ (1atm – 3atm)

= (5/2) ∙ 2000m³×10⁻⁶m³ ∙ (- 2 ∙ 1.01325×10⁵ Pa)

= -1013.25 J

B

Process B is a constant pressure process. The heat transferred in such a process equals the change in enthalpy of the gas.

Q = ∆H

Assuming ideal gas behavior the change in enthalpy of the nitrogen gas is given by:

∆H = n∙Cp∙∆T

The molar heat capacity at constant pressure for an diatomic ideal gas like nitrogen is

Cv = (7/2)∙R

Hence,

Q =∙(5/2)∙n∙R∙∆T

From ideal gas law

n∙R∙T = p∙V

follows for an constant pressure process:

n∙R∙∆T = ∆(p∙V) = p∙∆V

Hence,

Q =∙(7/2)∙p∙∆V = (5/2)∙p∙(V_f – V_i)

= (7/2) ∙ 2atm ∙ (3000cm³ – 1000cm³)

= (7/2) ∙ 2∙1.01325×10⁵ Pa ∙ 2000m³×10⁻⁶m³

= 1418.55 J