Question

Which of the following is true regarding a bucket of boiling water and a cup of boiling water.
I. The temperature of the two is the same.
II. The heat content of the two is the same.
III. The bucket of water contains more heat and is therefore hotter.
A) I only
B) II only
C) I and II only
D) I and III only

Answer 1

Hint: The statements given in the question once we analyse the relations between the temperature, heat and the amount of water. The three quantities are related together to each other in the thermodynamic formulae for specific heat capacity.

Complete step by step answer:
We are given a cup of boiling water and a bucket of boiling water. Obviously, we know that the amount of water in the two containers are not equal. The mass of the quantity of water in the bucket is greater than the mass of the water in the cup. Therefore, we have -
\[{{m}_{c}}<{{m}_{b}}\]
Now, let us consider the temperature of the boiling water in the cup and the bucket. We know that the temperature at which the water boils is always constant at the normal pressure conditions. It is independent of the quantity of water. Therefore, we know that both the temperatures are the same.
Now, consider the heat involved in the containers. According to the formula for specific heat capacity –
\[\Delta Q=ms\Delta T\]
We know that the quantities s and \[\Delta T\] on the R.H.S are same for both the cup and the bucket; therefore, the heat is directly proportional to the mass of the liquid –
\[\Delta {{Q}_{c}}<\Delta {{Q}_{b}}\]
From the above observation, we get that the heat involved will be greater for the water boiling in the bucket.

So, the correct answer is “Option D”.

Note: We should be careful not to mix up with the terms-temperature and the heat. The temperature is the measure of heat, whereas heat is the amount of energy in a system. The heat is directly related to the amount of substance whereas, the temperature is independent of mass.