Thermal Properties of Matter - Numerical Problems

The temperature of water in a beaker is 50°C, what is its value on the Fahrenheit scale? (122°F)

Difficulty: Easy

Solution:   Temperature in Celsius scale = C = 50°C                     The temperature on the Fahrenheit scale = F =?                     F = 1.8C + 32                     F = $1.8 \times $ 50 + 32 = 90 + 32                     F = 122°F

Normal human body temperature is 98.6°F, convert it into Celsius scale and Kelvin scale. (37°C,310K)

Difficulty: Easy

Solution:    The temperature on Fahrenheit scale = 98.6°F The temperature on the Celsius scale =? The temperature on the Kelvin scale =?   F = 1.8C + 32 1.8C = F – 32 1.8C = 98.6 -32 1.8C = 66.6 C =$\frac{(66.6)}{(1.8)}$ = 37°C   T(K) = C + 273 T(K) = 37 + 273 T(K) = 310K

Calculate the increase in the length of an aluminum bar 2 m long when heated from 0°C to 20°C, if the thermal coefficient of linear expansion of aluminum is $2.5 \times 〖10〗^{-5} K^{-1}$. (0.1cm)

Difficulty: Easy

Solution:       Original length of rod = $L_{(0=)}$ 2m                  Initial temperature = $T_{(0=)}$  0°C = 0 + 273 = 273 K              Final temperature = T =  20°C = 20 + 273 = 293 K           Change in temperature = $\triangle T$   = $T - T_{0}$ = 293 – 273 = 20 K         Coefficient of linear expansion of aluminum = α = $2.5 \times 10^{-5} K^{-1}$             Increase in volume $\triangle L$ = ?                                      $ \triangle L = α L_0 \triangle$ T                                           $\triangle L = 2.5 \times 10^{-5} \times20$                                       $\triangle L = 100 \times 10^{-5}$                $\triangle L = 0.001 m = 0.001\times$ 100 = 0.1cm

Numerical Problems