A Carnot type engine has a reservoir of 1000 K with an efficiency of 50%. Find the temperature of the sink.
Let T1 be the sink temperature and T2 be the heat reservoir temperature.
Carnot Efficiency = 1 - (T1/T2)
0.5 = 1 - T1/T2
T1 = 0.5*T2 = 500 K
To find the temperature of the sink in a Carnot-type engine, we can use the equation for the efficiency of a Carnot engine:
Efficiency = (T_hot - T_cold) / T_hot
Where:
- Efficiency is given as 50% or 0.50 (in decimal form)
- T_hot is the temperature of the hot reservoir
- T_cold is the temperature of the cold reservoir or sink (what we need to find)
We know that the efficiency is 0.50, so we can substitute these values into the equation:
0.50 = (1000 K - T_cold) / 1000 K
Next, we can cross-multiply to isolate T_cold:
0.50 * 1000 K = 1000 K - T_cold
500 K = 1000 K - T_cold
Now, we can isolate T_cold by subtracting 1000 K from both sides of the equation:
T_cold = 1000 K - 500 K
T_cold = 500 K
Therefore, the temperature of the sink is 500 Kelvin.