Answer the following : (d) What is the temperature of the triple-point of water on an absolute scale whose unit interval size is equal to that of the Fahrenheit scale ?

Explain why : (b) a brass tumbler feels much colder than a wooden tray on a chilly day

A brass wire 1.8 m long at 27 °C is held taut with little tension between two rigid supports. If the wire is cooled to a temperature of –39 °C, what is the tension developed in the wire, if its diameter is 2.0 mm ? Co-efficient of linear expansion of brass = $2.0 \times 10^{-5} K^{-1}$; Young’s modulus of brass = $0.91 \times 10^{11}$ Pa.

Answer the following questions based on the P – T phase diagram of $CO_2$: (c) Describe qualitatively the changes in a given mass of solid $CO_2$ at 10 atm pressure and temperature –65 °C as it is heated up to room temperature at constant pressure.

Explain why : (d) the earth without its atmosphere would be inhospitably cold

A brass rod of length 50 cm and diameter 3.0 mm is joined to a steel rod of the same length and diameter. What is the change in length of the combined rod at 250 °C, if the original lengths are at 40.0 °C? Is there a ‘thermal stress’ developed at the junction ? The ends of the rod are free to expand (Co-efficient of linear expansion of brass = $2.0 \times 10^{-5} K^{-1}$, steel = $1.2 \times 10^{-5} K^{-1}$ ).

Answer the following : (b) There were two fixed points in the original Celsius scale as mentioned above which were assigned the number 0 °C and 100 °C respectively. On the absolute scale, one of the fixed points is the triple-point of water, which on the Kelvin absolute scale is assigned the number 273.16 K. What is the other fixed point on this (Kelvin) scale ?

A steel tape 1m long is correctly calibrated for a temperature of 27.0 °C. The length of a steel rod measured by this tape is found to be 63.0 cm on a hot day when the temperature is 45.0 °C. What is the actual length of the steel rod on that day ? What is the length of the same steel rod on a day when the temperature is 27.0 °C ? Coefficient of linear expansion of steel = $1.20 \times 10^{-5} K^{-1}$.

A child running a temperature of 101°F is given an antipyrin (i.e. a medicine that lowers fever) which causes an increase in the rate of evaporation of sweat from his body. If the fever is brought down to 98 °F in 20 minutes, what is the average rate of extra evaporation caused, by the drug. Assume the evaporation mechanism to be the only way by which heat is lost. The mass of the child is 30 kg. The specific heat of human body is approximately the same as that of water, and latent heat of evaporation of water at that temperature is about $580 cal g^{-1}$.

Answer the following : (c) The absolute temperature (Kelvin scale) $T$ is related to the temperature $t_c$ on the Celsius scale by $t_c = T – 273.15$. Why do we have 273.15 in this relation, and not 273.16 ?

Answer the following questions based on the P-T phase diagram of carbon dioxide: (b) What is the effect of decrease of pressure on the fusion and boiling point of $CO_2$ ?

The electrical resistance in ohms of a certain thermometer varies with temperature according to the approximate law : $R = R_o [1 + \alpha (T – T_o )]$. The resistance is 101.6 $\Omega$ at the triple-point of water 273.16 K, and 165.5 $\Omega$ at the normal melting point of lead (600.5 K). What is the temperature when the resistance is 123.4 $\Omega$ ?

Answer the following questions based on the P-T phase diagram of carbon dioxide: (a) At what temperature and pressure can the solid, liquid and vapour phases of $CO_2$ co-exist in equilibrium ?

Given below are observations on molar specific heats at room temperature of some common gases.
Gas Molar specific heat ($C_v$) ($cal mol^{-1} K^{-1}$)
Hydrogen 4.87
Nitrogen 4.97
Oxygen 5.02
Nitric oxide 4.99
Carbon monoxide 5.01
Chlorine 6.17
The measured molar specific heats of these gases are markedly different from those for monatomic gases. Typically, molar specific heat of a monatomic gas is 2.92 cal/mol K. Explain this difference. What can you infer from the somewhat larger (than the rest) value for chlorine ?

A brass boiler has a base area of 0.15 $m^2$ and thickness 1.0 cm. It boils water at the rate of 6.0 kg/min when placed on a gas stove. Estimate the temperature of the part of the flame in contact with the boiler. Thermal conductivity of brass = $109 J s^{-1} m^{-1} K^{-1}$ ; Heat of vaporisation of water = $2256 \times 10^3 J kg^{-1}$.

Answer the following : (a) The triple-point of water is a standard fixed point in modern thermometry. Why ? What is wrong in taking the melting point of ice and the boiling point of water as standard fixed points (as was originally done in the Celsius scale) ?

Two ideal gas thermometers A and B use oxygen and hydrogen respectively. The following observations are made :
Temperature Pressure thermometer A Pressure thermometer B
Triple-point of water $1.250 \times 10^5$ Pa $0.200 \times 10^5$ Pa
Normal melting point of sulphur $1.797 \times 10^5$ Pa $0.287 \times 10^5$ Pa
(a) What is the absolute temperature of normal melting point of sulphur as read by thermometers A and B ?

A ‘thermacole’ icebox is a cheap and an efficient method for storing small quantities of cooked food in summer in particular. A cubical icebox of side 30 cm has a thickness of 5.0 cm. If 4.0 kg of ice is put in the box, estimate the amount of ice remaining after 6 h. The outside temperature is 45 °C, and co-efficient of thermal conductivity of thermacole is $0.01 J s^{-1} m^{-1} K^{-1}$. [Heat of fusion of water = $335 \times 10^3 J kg^{-1}$]

Two ideal gas thermometers A and B use oxygen and hydrogen respectively. The following observations are made :
Temperature Pressure thermometer A Pressure thermometer B
Triple-point of water $1.250 \times 10^5$ Pa $0.200 \times 10^5$ Pa
Normal melting point of sulphur $1.797 \times 10^5$ Pa $0.287 \times 10^5$ Pa
(b) What do you think is the reason behind the slight difference in answers of thermometers A and B ? (The thermometers are not faulty). What further procedure is needed in the experiment to reduce the discrepancy between the two readings ?

A 10 kW drilling machine is used to drill a bore in a small aluminium block of mass 8.0 kg. How much is the rise in temperature of the block in 2.5 minutes, assuming 50% of power is used up in heating the machine itself or lost to the surroundings. Specific heat of aluminium = $0.91 J g^{-1} K^{-1}$.