An ideal gas is taken through a Carnot cycle. The isothermal expansion occurs at 290°C, and the isothermal compression takes place at 50.0°C

Question

An ideal gas is taken through a Carnot cycle. The isothermal expansion occurs at 290°C, and the isothermal compression takes place at 50.0°C. The gas takes in 1.36 103 J of energy from the hot reservoir during the isothermal expansion. Find the energy expelled to the cold reservoir in each cycle and the net work done by the gas in each cycle.

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Verity 4 years 2021-08-14T19:04:06+00:00 1 Answers 38 views 0

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  1. RuslanHeatt
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    2021-08-14T19:05:09+00:00
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    Answer:

    the energy expelled to the cold reservoir in each cycle = 0.78×10³ J

    the net work done by the gas in each cycle = 0.58 × 10³ J

    Explanation:

    Given that the isothermal expansion occurs at T_h = 290^0C

    = (290+273)K

    = 563 K

    Isothermal compression T_c  occurs at 50°C

    = (50+273)K

    = 323 K

    The amount of energy absorbed by the gas from the hot reservoir Q_h = 1.36*10^3 J

    a) The amount of energy expelled to the cold reservoir in each cycle can be calculated by using the formula:

    |Q_c|=|Q_h|(\frac{T_c}{T_h} )

    |Q_c|=(1.36*10^3J)(\frac{323}{563} )

    = 780.25

    = 0.78×10³ J

    b) the net work done by the gas in each cycle is as follows:

    W = |Q_h|-|Q_c|

    W = (1.36*10^3J)-(0.78*10^3J)

    W = 580

    W = 0.58 × 10³ J

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