1. Two thermometers are identical in every respect except that one has a spherical bulb and the other cylindrical bulb of same volume. Which one is more sensitive?

The thermometer with a cylindrical bulb is more sensitive.

For a body of a fixed volume, the surface area is least when it is spherical. Therefore, the cylindrical bulb has a bigger surface area than the other one and hence absorbs more heat in a given time compared to the other. So, the thermometer with cylindrical bulb responds quickly.

2. A piece of green glass is placed in a furnace and then taken out when it is heated. It is seen to be glowing with red light. – Why?

Green and red are the complementary colors. Therefore when the red light is absorbed by a body, illuminated with white light (containing all the colors) it appears green to us. The consequence of Kirchhoff’s law (or radiation) is that a good absorber of radiation is also a good radiator and vice versa. Therefore, when this piece of glass is taken out of the furnace it radiates out its heat through the wavelength of red light.

3. Two persons ordered for tea in a cafe while waiting for a third friend. One of them immediately poured tea in his cup and mixed cold milk with it. The other person poured tea immediately but mixed cold milk after the friend arrived. Who drinks warmer tea? – Explain.

The person who mixes tea with cold milk before the arrival of their friend drinks warmer tea.

Newton’s law of cooling can explain this. According to this law the rate of heat loss from a hot body is higher if its temperature difference with the surrounding is higher. Mixing of cold milk lowers the temperature of tea at the beginning of their wait. Therefore the temperature difference between this mixture and the surrounding is less compared to the tea in other cup and hence this tea looses less heat in the same time. As a result this tea remains warmer.

4. A beaker is filled with water at . What will happen to the water (or water level) if we heat it? What will happen if we lower the temperature?

Both for the rise or fall in temperature the water in the beaker will overflow. Water at has maximum density and hence its volume is minimum. Therefore if we heat the water at this temperature, it expands in volume and overflows.

5. A hollow iron-ball floats in water at in fully submerged condition. What will happen if the temperature of water is rises to ?

The iron-ball will sink in water at .

At the weight of the ball is just equal to the weight of the displaces water. With the rise in temperature both the ball and water expand but the expansion of liquid is relatively bigger than that of the metal (here, iron). So, effectively we should consider the expansion of water as a net result. Due to the expansion of water, its density will decrease and the buoyant force cannot balance the weight of the ball any more. Therefore the iron-ball sinks at a higher temperature like .

6. Why a gas has two specific heats, while solids and liquids have only one specific heat?

The expansion or compression of solid and liquid with the rise or fall in temperature is not very significant compared to the change of volume with the change of temperature in case of a gas. If the volume remains constant during the rise in temperature of a fixed mass of a gas, then the gas does not do any external work. But if the pressure remains constant, the volume changes considerably for a rise in temperature. In this case the gas does some external work, which we cannot ignore. Clearly, for a fixed mass (say, ) of gas heat required to raise the temperature by is bigger if the pressure remains constant compared to when the volume remains fixed. For this reason we get two distinctly different values for the specific heat of a gas.

7. Why is the specific heat of a gas at constant pressure () greater than its specific heat at constant volume ()?

The relation among the supplied heat (), change in internal energy () and work done () for a fixed mass of gas is:

In case of determining , we supply the heat only to change the temperature i.e. to change the internal energy of the gas keeping its volume fixed. In this case . Therefore the gas does not require any heat to do the work during the rise in temperature. In case of determining , we supply the heat that raises the temperature of the gas as well as does some work (). Therefore the required heat is bigger than that in the previous case. Hence .