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Standard XII

Physics

Specific Heat Capacity

A new tempera...

Question

A new temperature scale uses $X$ as a unit of temperature, where the numerical value of the temperature $t_{x}$ in this scale is related to the absolute temperature $T$ by $t_{x} = 3 T + 300$ . If the specific heat of a material using this unit is $1400 J k g^{- 1} X^{- 1}$ its specific heat in the S.I. system of units is :

4200 J k g^{- 1} K^{- 1}

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1400 J k g^{- 1} K^{- 1}

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466.7 J k g^{- 1} K^{- 1}

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Impossible to determine from the information provided

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Solution

The correct option is B $4200 J k g^{- 1} K^{- 1}$
Given : $S = 1400$ $J k g^{- 1} X^{- 1}$
The equation $t_{x} = 3 T + 300$ $⟹$ $1$ $X = 300$ $K$
Thus Specific heat in SI unit $S^{'} =$ $1400$ $J k g^{- 1} X^{- 1} \times 300 \frac{X}{K} = 4200$ $J k g^{- 1} K^{- 1}$

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A new temperature scale uses X as a unit of temperature, where the numerical value of the temperature tx in this scale is related to the absolute temperature T by tx=3T+300. If the specific heat of a material using this unit is 1400Jkg−1X−1 its specific heat in the S.I. system of units is :

The correct option is B 4200Jkg−1K−1Given : S=1400 Jkg−1X−1 The equation tx=3T+300 ⟹ 1 X=300 KThus Specific heat in SI unit S′= 1400 Jkg−1X−1×300XK=4200 Jkg−1K−1

The correct option is B $4200 J k g^{- 1} K^{- 1}$
Given : $S = 1400$ $J k g^{- 1} X^{- 1}$
The equation $t_{x} = 3 T + 300$ $⟹$ $1$ $X = 300$ $K$
Thus Specific heat in SI unit $S^{'} =$ $1400$ $J k g^{- 1} X^{- 1} \times 300 \frac{X}{K} = 4200$ $J k g^{- 1} K^{- 1}$