How much heat is required to raise the temperature of $ 2 \, kg $ of water from $ 20^\circ C $ to $ 80^\circ C $? (Specific heat capacity of water = $ 4200 \, J/kg^\circ C $)

Question

Two gases A and B are filled at the same pressure in separate cylinders with movable pistons of radii $r_A$ and $r_B$ respectively. On supplying an equal amount of heat to both the cylinders, their pressures remain constant and their pistons are displaced by 16 cm and 9 cm respectively. If the change in their internal energies is the same, then the ratio $r_A / r_B$ is:

Answer 1

The heat energy $ Q $ required to increase the temperature of water is calculated using the formula $ Q = mc\Delta T $. In this formula, $ Q $ represents heat energy in Joules, $ m $ is the mass of the water in kilograms, $ c $ is the specific heat capacity in J/kg°C, and $ \Delta T $ is the temperature change in °C.

The provided data includes:

$ m = 2 \, kg $,
$ c = 4200 \, J/kg^\circ C $,
Initial temperature $ T_1 = 20^\circ C $,
Final temperature $ T_2 = 80^\circ C $.

The temperature change $ \Delta T $ is determined by subtracting the initial temperature from the final temperature: $ \Delta T = T_2 - T_1 = 80^\circ C - 20^\circ C = 60^\circ C $.

The formula is applied with the given values: $ Q = 2 \times 4200 \times 60 $.

The calculation proceeds as follows:

First, multiply mass by specific heat capacity: $ 2 \times 4200 = 8400 $.
Then, multiply the result by the temperature change: $ 8400 \times 60 = 504000 \, J $.

Consequently, $ 504000 \, J $ of heat is necessary to elevate the temperature of 2 kg of water from $ 20^\circ C $ to $ 80^\circ C $.

How much heat is required to raise the temperature of $ 2 \, kg $ of water from $ 20^\circ C $ to $ 80^\circ C $? (Specific heat capacity of water = $ 4200 \, J/kg^\circ C $)

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The Correct Option is A

Solution and Explanation

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