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Question: Two beakers A and B contain 100g of water and 100g of alcohol at \(70{}^\circ \)C. The total heat en...

Two beakers A and B contain 100g of water and 100g of alcohol at 70∘70{}^\circ C. The total heat energy contained in beaker
A. A is more than beaker B
B. A is less than beaker B
C. A and B is the same
D. None of these

Explanation

Solution

Hint: Here we have to compare the heat energies of the two liquids of same mass and at the same temperature so we can use the formula Q=mcΔTQ=mc\Delta T and since the other quantities are the same we just need to compare the specific heat of water and alcohol.

Complete step by step answer:
The heat energy added or removed from a substance of mass m and specific heat capacity c and the change in temperature is ΔT\Delta T, is given by Q:
Q=mcΔTQ=mc\Delta T
Since the mass for both water and alcohol is 100g and the temperature is 70∘70{}^\circ C we just have to compare the specific heat of alcohol and water.
Experimentally it is seen that the value of specific heat for Alcohol is approximately 2.5(kJ/(kg K))2.5\left( kJ/\left( kg\text{ }K \right) \right) and for water it is approximately 4(kJ/(kg K))4\left( kJ/\left( kg\text{ }K \right) \right). Since c is greater for water then alcohol the total heat energy for water would be greater than alcohol.
Hence, the correct answer is option A. A is more than beaker B

Note: Students should also note that since the density of water is greater than alcohol it would have more molecules in a unit volume than alcohol that will result in less interatomic spacing and thus, greater kinetic energy and more will be the heat energy in water than alcohol.