The exhaust temperature of a heat engine is 250∘C .What must be the high temperature if the Carnot efficiency is to be 35% ?
How much heat (in joules) is required to raise the temperature of 39.0kg of water from 25∘C to 95∘C? The specific heat of water is 4186 J/kg⋅C∘.
To determine the high temperature required for the Carnot efficiency to be 35%, we need to use the formula for Carnot efficiency:
Carnot efficiency = 1 - (T_low / T_high),
where T_low and T_high are the temperatures in Kelvin.
To convert the given exhaust temperature of 250∘C to Kelvin, we use the conversion formula:
T_kelvin = T_celsius + 273.15,
where 250∘C is equal to 523.15K.
Let's represent the unknown high temperature as T_high in Kelvin.
Using the Carnot efficiency formula, we can write:
0.35 = 1 - (523.15 / T_high).
To solve for T_high, we rearrange the equation:
523.15 / T_high = 1 - 0.35.
Simplifying the equation:
523.15 / T_high = 0.65.
Cross multiply:
T_high = 523.15 / 0.65.
Calculating the value:
T_high ≈ 805K.
Therefore, the high temperature required for the Carnot efficiency to be 35% is approximately 805 Kelvin.