Question

The coefficient of apparent expansion of mercury in a glass vessel is 153 × 10⁻⁶/°C and in a steel vessel is 144 × 10⁻⁶/°C. If a for steel is 12 × 10⁻⁶/°C, then, that of glass is(a) 9 × 10⁻⁶/°C(b) 6 × 10⁻⁶/°C(c) 36 × 10⁻⁶/°C(d) 27 × 10⁻⁶/°C

Answer 1

Answer: (a). The value of a for glass is $a_{glass} = 9\times10^{-6}/^{o}C$.

Explanation:

Given that,

Coefficient of apparent expansion of mercury in a glass vessel $\alpha_{g} = 153\times10^{-6}/^{o}C$

Coefficient of apparent expansion of mercury in a steel vessel $\alpha_{s} = 144\times10^{-6}/^{o}C$

The value of a for steel $a_{s} = 12\times10^{-6}/^{o}C$

We know that,

$\alpha_{real} = \alpha_{app}+\alpha_{vessel}$

So, for glass and steel

$(\alpha_{app}+\alpha_{vessel})_{glass} = (\alpha_{app}+\alpha_{vessel})_{steel}$

Where, $\alpha_{vessel} = 3a$

$(\alpha_{app}+3a)_{glass} = (\alpha_{app}+3a})_{steel}$

$(153\times10^{-6}/^{o}C +3a)_{glass} = (144\times10^{-6}/^{o}C+3\times 12\times10^{-6}/^{o}C})_{steel}$

$3a_{glass} = 144\times10^{-6}/^{o}C +36\times10^{-6}/^{o}C - 153\times10^{-6}/^{o}C$

$a_{glass} = 9\times10^{-6}/^{o}C$

Hence, the value of a for glass is $a_{glass} = 9\times10^{-6}/^{o}C$.