Q.3. In a rectangular coordinate object, an equation for the temperature distribution constructed as T(x) = -20T + 60 (T in °C and x in cm) Give an example with a full information data (i.e. including thickness, boundary temperatures with the help of a sketch) which can satisfy the above equation.
how the temperature distribution across different flat and cylindrical contacting solids varies with pressure.
The sketch of the mentioned equation in the question is to be plot along with proper data and example.
The equation given in the question is slightly incorrect. As temperature T is given as a function of the boundary thickness x, the correct equation must be,
T = -20x + 60 ....... (1)
T is the boundary temperature in degree Celsius
x is the boundary thickness in centimetre
In the above equation (1), it can be seen that the equation is of straight line with negative slope.
Let us assume the different values of the boundary thickness x and corresponding to each value of x, find the boundary temperature T.
At x = 0, T = -20(0) + 60 = 600C
At x = 1, T = -20(1) + 60 = 400C
At x = 2, T = -20(2) + 60 = 200C
At x = 3, T = -20(3) + 60 = 00C
At x = 4, T = -20(4) + 60 = -200C
At x = 5, T = -20(5) + 60 = -400C
At x = 6, T = -20(6) + 60 = -600C
At x = 7, T = -20(7) + 60 = -800C
At x = 8, T = -20(8) + 60 = -1000C
At x = 9, T = -20(9) + 60 = -1200C
At x = 10, T = -20(10) + 60 = -1400C
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