Two absolute scales \(A \) and \(B,\) have triple points of water defined to be \(200 A\) and \(350 B\). The relationship between \(T_A \) and \(T_B\):
1. \(T_A = {5 \over 7}T_B\)
2. \(T_A = { 4 \over 7}T_B\)
3. \(T_A = { 6 \over 7}T_B\)
4. \(T_A = T_B\)

The electrical resistance in ohms of a certain thermometer varies with temperature according to the approximate law:

$\mathrm{R}={\mathrm{R}}_0\left[1+\mathrm{\alpha }\left(\mathrm{T}-{\mathrm{T}}_0\right)\right]$

The resistance is 101.6 Ω at the triple-point of water 273.16 K, and 165.5 Ω at the normal melting point of lead (600.5 K). What is the temperature when the resistance is 123.4 Ω?

$\left(1\right) 384.8 \mathrm{K}$
$\left(2\right) 486.8 \mathrm{K}$
$\left(3\right) 287.61 \mathrm{K}$
$\left(4\right) 185.61 \mathrm{K}$

A steel tape \(1\) m long is correctly calibrated for a temperature of \(27^\circ \text{C}\). 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 \(45^\circ \text{C}\). What is the actual length of the steel rod on that day?
(Coefficient of linear expansion of steel = \(1.20\times 10^{-5}~\text{K}^{-1}\)).
1. \( 62.485 \) cm
2. \( 60.762 \) cm
3. \( 65.935 \) cm
4. \( 63.013\) cm

A large steel wheel is to be fitted onto a shaft of the same material. At 27 °C, the outer diameter of the shaft is 8.70 cm and the wheel's central hole has a diameter of 8.69 cm. The shaft is cooled using ‘dry ice’. At what temperature of the shaft does the wheel slip on the shaft?
(Assume the coefficient of linear expansion of the steel to be constant over the required temperature range  and \(\alpha\) steel = \(1.20 \times 10^{-5} K^{-1}\))
1. 68°C
2. -70°C
3.  -69°C
4. -67°C

A geyser heats water flowing at the rate of 3.0 liters per minute from 27 °C to 77 °C. If the geyser operates on a gas burner, what is the fuel consumption rate if its heat of combustion is $4.0\times {10}^4 J/g$?

1. 15.7 g per min
2. 15.10 g per min
3. 14.39 g per min
4. 17.11 g per min

A hole is drilled in a copper sheet. The diameter of the hole is 4.24 cm at 27.0 °C. What is the change in the diameter of the hole when the sheet is heated to 227 °C?

(Co-efficient of linear expansion of copper= $1.70\times {10}^{-5} {\mathrm{K}}^{-1}$)

1. 0.0144 cm
2. 0.0234 cm
3. 0.0123 cm
4. 0.0111 cm

A brass wire \(1.8\) m long at \(27\) °C is held taut with a little tension between two rigid supports. If the wire is cooled to a temperature of\(-39\) °C, what is the tension created in a wire with a diameter of \(2.0\) mm? (coefficient of linear expansion of brass \(=2.0 \times10^{-5}\) K^–1, Young's modulus of brass\(=0.91 \times10^{11}\) Pa)
1. \(3.8 \times 10^3\) N
2. \(3.8 \times 10^2\) N
3. \(2.9 \times 10^{-2}\) N
4. \(2.9 \times 10^{2}\) N

The coefficient of volume expansion of glycerine is \(49\times 10^{-5}\) K^–1. What is the fractional change in its density for a \(30^\circ \text{C}\) rise in temperature?
1. \(1.44\times10^{-3}\)
2. \(1.57\times10^{-3}\)
3. \(1.57\times10^{-2}\)
4. \(1.44\times10^{-2}\)

A body cools from \(80\) °C to \(50\) °C in \(5\) minutes. The time it takes to cool from \(60\) °C to \(30\) °C is:
(The temperature of the surroundings is \(20\) °C)
1. \(13\) min
2. \(15\) min
3. \(12\) min
4. \(10\) min

A brass boiler has a base area of 0.15 $m^2$ and a thickness of 1.0 cm. It boils water at a rate of 6.0 kg/min when placed on a gas stove. What is the temperature of the part of the flame in contact with the boiler?
(Thermal conductivity of brass = $109 J s^{-1} m^{-1} K^{-1}$, the heat of vaporization of water =$2256\times {10}^3 J/kg$.)
1. 237.98°C
2. 150°C
3. 137.98°C
4. 100°C