A certain Carnot engine has T_h = T_c + 35K, and an efficiency of 20.0%. What is T_h? A) 70.0 K B) 140 K C) 175 K D) 210 K E) 245 K

Question

Quizplus · Accepted Answer

We can start by using the equation for the efficiency of a Carnot engine:

efficiency = 1 - (T2/T1)

where T2 is the temperature of the cold reservoir and T1 is the temperature of the hot reservoir.

We are given that the efficiency of this Carnot engine is 20.0%, or 0.20. Therefore, we can write:

0.20 = 1 - (T2/T1)

Solving for T2/T1, we get:

T2/T1 = 0.80

We are also given that:

TS1U1B1hS1U1B0 = TS1U1B1cS1U1B0 + 35K

This tells us that the temperature of the hot reservoir (TS1U1B1h) is 35 K higher than the temperature of the cold reservoir (TS1U1B1c). We can use these values to set up equations for T1 and T2:

T1 = TS1U1B1hS1U1B0
T2 = TS1U1B1cS1U1B0

Using T2/T1 = 0.80, we can solve for T2:

T2 = (0.80)T1

Substituting in the values for T1 and T2 in terms of the given temperatures, we get:

TS1U1B1cS1U1B0 = T2 = (0.80)T1 = (0.80)(TS1U1B1hS1U1B0)
TS1U1B1hS1U1B0 = TS1U1B1cS1U1B0 + 35K

Substituting the first equation into the second equation, we get:

TS1U1B1hS1U1B0 = (0.80)(TS1U1B1hS1U1B0) + 35K

Solving for TS1U1B1hS1U1B0, we get:

TS1U1B1hS1U1B0 = 175K

Therefore, the answer is C.

A Certain Carnot Engine Has Th = Tc + 35K

A Certain Carnot Engine Has T_h = T_c + 35K