Heat and Mass Transfer
The logarithmic mean temperature difference (tm) is given by (where Δt1 and Δt2 are temperature differences between the hot and cold fluids at entrance and exit)

tm = loge (Δt1/Δt2)/ (Δt1 - Δt2)
tm = tm = (Δt1 - Δt2) loge (Δt1/Δt2)
tm = loge (Δt1 - Δt2)/ Δt1/Δt2
tm = (Δt1 - Δt2)/ loge (Δt1/Δt2)

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Heat and Mass Transfer
The time constant of a thermocouple is

Determined by the time taken to reach 100°C from 0°C
The time taken to attain 63.2% of the value of initial temperature difference
The time taken to attain 50% of the value of initial temperature difference
The time taken to attain the final temperature to be measured

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