Tanya heats 100 g of a liquid with an electric heater which has a constant power output of 60 W. After 100 s the rise in temperature is 40 K. The specific heat capacity of the liquid in Jkg−1K−1 is calculated from which of the following?
Question
Tanya heats 100 g of a liquid with an electric heater which has a constant power output of 60 W. After 100 s the rise in temperature is 40 K. The specific heat capacity of the liquid in Jkg−1K−1 is calculated from which of the following?
Solution
The specific heat capacity (c) of a substance can be calculated using the formula:
Q = mcΔT
where: Q is the heat energy absorbed or released (in joules, J), m is the mass of the substance (in kilograms, kg), c is the specific heat capacity (in joules per kilogram per kelvin, Jkg−1K−1), ΔT is the change in temperature (in kelvin, K).
In this case, we know that:
- The power output of the heater (P) is 60 W, which is equivalent to 60 J/s.
- The heater is used for 100 s, so the total energy supplied (Q) is P * time = 60 J/s * 100 s = 6000 J.
- The mass of the liquid (m) is 100 g, which is equivalent to 0.1 kg.
- The change in temperature (ΔT) is 40 K.
We can substitute these values into the formula to find the specific heat capacity:
6000 J = 0.1 kg * c * 40 K
Solving for c gives:
c = 6000 J / (0.1 kg * 40 K) = 1500 Jkg−1K−1
So, the specific heat capacity of the liquid is 1500 Jkg−1K−1.
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