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Standard XII

Physics

Area and Volume Expansion

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 $1400 J k g^{- 1} K^{- 1}$ 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 A $4200 J k g^{- 1} K^{- 1}$
$t_{x} = 3 T + 00$
If in SI system the temperature has to be changed by one unit then in the given side the temperature has to be changed by three units .
Thus the specific heat which is the heat required to change the temperature of the body by $1$ unit will be changed on the other side by $3$ units.
So specific heat in SI scale $= 3 (1400) = 4200 J / K g K$

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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−1K−1 its specific heat in the S.I. system of units is :