An ideal engine has an efficiency of 0.725 and uses gas from a hot reservoir at a temperature of \(622 \mathrm{K}\). What is the temperature of the cold reservoir to which it exhausts heat?

Short Answer

Expert verified
Based on the given efficiency of 0.725 and a hot reservoir temperature of 622 K, the temperature of the cold reservoir for an ideal engine is approximately 275 K.

Step by step solution

01

Write down the given information

We are given: - Efficiency (\(\eta\)): 0.725 - Temperature of hot reservoir (\(T_h\)): 622 K
02

Find the temperature of the cold reservoir using the Carnot efficiency formula

We can use the equation \(\eta = 1 - \frac{T_c}{T_h}\) and solve for the temperature of the cold reservoir, \(T_c\). First, plug in the given values: \(0.725 = 1 - \frac{T_c}{622}\)
03

Solve for \(T_c\)

To solve for \(T_c\), first subtract 1 from both sides of the equation: \(0.725 - 1 = - \frac{T_c}{622}\) Now, multiply both sides of the equation by 622: \((0.725 - 1) \times 622 = -T_c\) Next, simplify the equation: \(-275 \approx -T_c\) Finally, multiply both sides by -1: \(T_c \approx 275 \mathrm{K}\)
04

State the final answer

The temperature of the cold reservoir to which the ideal engine exhausts heat is approximately \(275 \mathrm{K}\).

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