Physics Heat transfer question (will award BEST ANSWER)?

SOMEONE ASKED πŸ‘‡

Physics Heat transfer question (will award BEST ANSWER)?

HERE THE ANSWERS πŸ‘‡

  • 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 = βˆ†U

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

    βˆ†U = nβˆ™Cvβˆ™βˆ†T

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

    Cv = (5/2)βˆ™R

    Hence,

    Q =βˆ™(5/2)βˆ™nβˆ™Rβˆ™βˆ†T

    From ideal gas law

    nβˆ™Rβˆ™T = pβˆ™V

    follows for an constant volume process:

    nβˆ™Rβˆ™βˆ†T = βˆ†(pβˆ™V) = Vβˆ™βˆ†p

    Hence,

    Q =βˆ™(5/2)βˆ™Vβˆ™βˆ†p = (5/2)βˆ™Vβˆ™(p_f – p_i)

    = (5/2) βˆ™ 2000cmΒ³ βˆ™ (1atm – 3atm)

    = (5/2) βˆ™ 2000mΒ³Γ—10⁻⁢mΒ³ βˆ™ (- 2 βˆ™ 1.01325Γ—10⁡ 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 = βˆ†H

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

    βˆ†H = nβˆ™Cpβˆ™βˆ†T

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

    Cv = (7/2)βˆ™R

    Hence,

    Q =βˆ™(5/2)βˆ™nβˆ™Rβˆ™βˆ†T

    From ideal gas law

    nβˆ™Rβˆ™T = pβˆ™V

    follows for an constant pressure process:

    nβˆ™Rβˆ™βˆ†T = βˆ†(pβˆ™V) = pβˆ™βˆ†V

    Hence,

    Q =βˆ™(7/2)βˆ™pβˆ™βˆ†V = (5/2)βˆ™pβˆ™(V_f – V_i)

    = (7/2) βˆ™ 2atm βˆ™ (3000cmΒ³ – 1000cmΒ³)

    = (7/2) βˆ™ 2βˆ™1.01325Γ—10⁡ Pa βˆ™ 2000mΒ³Γ—10⁻⁢mΒ³

    = 1418.55 J

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