= kS(T-Tm) where k < 0
Here Tm= 21°C and S is exposed surface area.
Here , where SA and SB are the exposed surface area of A-cup and B-cup respectively.
Therefore
= kSdt
Integrating,
= kS dt
=> ln(T-21) = kSt + C, C is integration constant.
Temperature are being measured in °C and time in minute here.
When t = 0 , initial temperature T = 65
So, ln(65 - 21) = C
=> C = ln(44)
So ln(T-21) = kSt + ln(44 )
So ln(T-21) - ln(44) = kSt
=> ln = kSt
For cup A, S = SA and T = 38 when t = 30
So equation for cup-A is
ln = 30kSA
=> ln = 30kSA •••••••••eq(1)
For cup-B, S = SB and T=? when t = 30
So equation for cup-B is
ln = 30kSB
ln = 60kSA as SB =2 SA ••••eq(2)
Comparing eq(2) and eq(1) we get
ln = 2 ln
=> ln = ln ( )2
=> =
=> T - 21 =
=> T = 21 + 6.568
=> T = 27.568
The temperature of coffee in cup B is 27.57 °C ( correct up to two decimal places)
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