Question

Газ в идеальной тепловой машины получает от нагревателя теплоту 42 кдж какую работу совершает газ , если абсолютная температура в три раза выше , чем температура холодильника. Какое количество теплоты газ отдает холодильнику?

Answer 1

Qн=42кДж
η=$\frac{A}{Q1} = \frac{Q1-Q2}{Q1} = \frac{T1-T2}{T1}$
Используем 1 и 3 формулы:
$\frac{A}{42} = \frac{3T-T}{3T}$
A=42кДж*2/3=28кДж
Используем 1 и 2 формулы:
$\frac{28}{42} = \frac{42-Q2}{42}$
Q2=42-28=14 кДж

Answer 2

Calculating Work and Heat Transfer in an Ideal Thermal Machine

In an ideal thermal machine, the gas receives 42 kJ of heat from the heater. We are given that the absolute temperature is three times higher than the temperature of the refrigerator. We need to calculate the work done by the gas and the amount of heat transferred to the refrigerator.

Work Done by the Gas: The work done by the gas in an ideal thermal machine can be calculated using the formula: \[ W = Q \times (1 - \frac{T_c}{T_h}) \]

Where: - \( W \) = Work done by the gas - \( Q \) = Heat received by the gas - \( T_c \) = Temperature of the refrigerator - \( T_h \) = Temperature of the heater

Substituting the given values: \[ W = 42 \times (1 - \frac{T_c}{3T_c}) \] \[ W = 42 \times (1 - \frac{1}{3}) \] \[ W = 42 \times \frac{2}{3} \] \[ W = 28 \, kJ \]

Heat Transferred to the Refrigerator: The amount of heat transferred to the refrigerator can be calculated using the formula: \[ Q_c = Q - W \]

Where: - \( Q_c \) = Heat transferred to the refrigerator - \( Q \) = Heat received by the gas - \( W \) = Work done by the gas

Substituting the given values: \[ Q_c = 42 - 28 \] \[ Q_c = 14 \, kJ \]

Therefore, the work done by the gas is 28 kJ, and the amount of heat transferred to the refrigerator is 14 kJ.

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