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 α for steel is 12 × 10^-6/°C, then that of glass is ______.

विकल्प

• 9 × 10^-6/°C

• 6 × 10^-6/°C

• 36 × 10^-6/°C

• 27 × 10^-6/°C

Answer 1

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 α for steel is 12 × 10^-6/°C, then that of glass is 9 × 10^-6/°C.

Explanation:

`gamma_"real"=gamma_"app"+gamma_"vessel"`

So `(gamma_"app"+gamma_"vessel")_"glass"=(gamma_"app"+gamma_"vessel")_"steel"`

⇒ 153 × 10^-6 + `(gamma_"vessel")_"glass"`

= 144 × 10^-6 + `(gamma_"vessel")_"steel"`

Further,

`(gamma_"vessel")_"steel"` 3α = 3 × (12 × 10^-6)

= 36 × 10^-6/°C

⇒ 153 × 10^-6 + `(gamma_"vessel")_"glass"`

= 144 × 10^-6 + 36 × 10^-6

`(gamma_"vessel")_"glass"` = 3α = 27 × 10^-6/°C

⇒ α = 9 × 10^-6/°C