(a) How much heat (J) flows from 1.00 kg of water at 46.0°C when it is placed in contact with 1.00 kg of 18°C water in reaching equilibrium?
(b) What is the change(J/K) in entropy due to this heat transfer?
(c) How much work (J) is made unavailable, taking the lowest temperature to be 18°C?
To answer these questions, we need to use the principles of heat transfer and thermodynamics. Let's break down each question and explain how to solve them step by step:
(a) How much heat (J) flows from 1.00 kg of water at 46.0°C when it is placed in contact with 1.00 kg of 18°C water in reaching equilibrium?
To calculate the heat transfer, we can use the equation:
Q = mcΔT
where Q is the heat transfer, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
For the first water at 46.0°C, the mass is 1.00 kg, and the specific heat capacity of water is approximately 4.184 J/g·°C. We need to convert the mass to grams, so 1.00 kg is equal to 1000 g.
ΔT is the final temperature minus the initial temperature, which is 18°C (final) - 46.0°C (initial) = -28.0°C.
Plugging in the values:
Q1 = (1000 g) * (4.184 J/g·°C) * (-28.0°C)
Q1 = -117,152 J
The negative sign indicates that heat is flowing out of the first water.
(b) What is the change (J/K) in entropy due to this heat transfer?
To calculate the change in entropy, we can use the equation:
ΔS = Q / T
where ΔS is the change in entropy, Q is the heat transfer, and T is the temperature.
First, we need to convert the temperatures to Kelvin. The initial temperature is 46.0°C + 273.15 = 319.15 K, and the final temperature is 18°C + 273.15 = 291.15 K.
Plugging in the values:
ΔS = -117,152 J / 319.15 K
ΔS ≈ -367.34 J/K
The negative sign indicates a decrease in entropy.
(c) How much work (J) is made unavailable, taking the lowest temperature as 18°C?
To determine the work made unavailable, we can use the equation:
W_unavailable = T * ΔS
where W_unavailable is the work made unavailable, T is the temperature, and ΔS is the change in entropy.
Taking the lowest temperature as 18°C, we convert it to Kelvin: 18°C + 273.15 = 291.15 K.
Plugging in the values:
W_unavailable = 291.15 K * (-367.34 J/K)
W_unavailable ≈ -106,825.61 J
The negative sign indicates that work is being lost or made unavailable.