Water of mass m gram is slowly heated to increase the temperature from to . The change in entropy of the water, given specific heat of water is , is [2025]

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Q.
Water of mass m gram is slowly heated to increase the temperature from $T_{1}$ to $T_{2}$ . The change in entropy of the water, given specific heat of water is $1 {Jkg}^{- 1} K^{- 1}$ , is [2025]

1 zero

2 $m (T_{2} - T_{1})$

3 $m \ln (\frac{T_{1}}{T_{2}})$

4 $m \ln (\frac{T_{2}}{T_{1}})$

Ans.
(4)

dQ = msdT

$d S = \frac{d Q}{T} = \frac{m s d T}{T}$

$△ S = \int \frac{m s d T}{T} = m s \ln \frac{T_{f}}{T_{i}}$

$△ S = m \ln \frac{T_{2}}{T_{1}} as s = 1$

Solution

Q.
Water of mass m gram is slowly heated to increase the temperature from $T_{1}$ to $T_{2}$ . The change in entropy of the water, given specific heat of water is $1 {Jkg}^{- 1} K^{- 1}$ , is [2025]

1 zero

2 $m (T_{2} - T_{1})$

3 $m \ln (\frac{T_{1}}{T_{2}})$

4 $m \ln (\frac{T_{2}}{T_{1}})$

Ans.
(4)

dQ = msdT

$d S = \frac{d Q}{T} = \frac{m s d T}{T}$

$△ S = \int \frac{m s d T}{T} = m s \ln \frac{T_{f}}{T_{i}}$

$△ S = m \ln \frac{T_{2}}{T_{1}} as s = 1$

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Solution

Q. Water of mass m gram is slowly heated to increase the temperature from T1 to T2. The change in entropy of the water, given specific heat of water is 1 Jkg–1 K–1, is [2025]

1 zero

2 m(T2–T1)

3 m ln (T1T2)

4 m ln (T2T1)

Ans. (4) dQ = msdT dS=dQT=msdTT △S=∫msdTT=ms ln TfTi △S=m ln T2T1 as s=1

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Q.
Water of mass m gram is slowly heated to increase the temperature from $T_{1}$ to $T_{2}$ . The change in entropy of the water, given specific heat of water is $1 {Jkg}^{- 1} K^{- 1}$ , is [2025]

2 $m (T_{2} - T_{1})$

3 $m \ln (\frac{T_{1}}{T_{2}})$

4 $m \ln (\frac{T_{2}}{T_{1}})$

Ans.
(4)

dQ = msdT

$d S = \frac{d Q}{T} = \frac{m s d T}{T}$

$△ S = \int \frac{m s d T}{T} = m s \ln \frac{T_{f}}{T_{i}}$

$△ S = m \ln \frac{T_{2}}{T_{1}} as s = 1$