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Question

Question: The fundamental interval of a thermometer \[x\] is arbitrarily divided into 40 equal and that of ano...

The fundamental interval of a thermometer xx is arbitrarily divided into 40 equal and that of another thermometry into 80 equal parts. If the freezing point of xx is marked 20C{20^ \circ}C and that of y is marked 0C{0^ \circ}C. What is the temperature on x when y indicates 70C{70^ \circ}C? What is the temperature in C^ \circ C?

Explanation

Solution

We know that the fundamental interval refers to the value of the difference in temperature between two fixed points on a temperature scale which is taken in order to define the scale. It is also defined as the difference between the values recorded in a thermometer at two fixed points.

Complete answer: We have been given in this question that x is divided arbitrarily into forty equal parts and eighty equal parts in another thermometer, which means one degree rise in temperature on x means the two degree rise in temperature of y. After that also if a temperature is marked zero degrees in y and twenty degrees in x then x is twenty steps ahead of y.
Therefore, 70C{70^ \circ}C in y means 35C{35^ \circ}C in x
Now as x is twenty steps ahead of y, 35 becomes 55
Hence, the correct solution is 55C{55^ \circ }C.

Note: One point to be noted is to do the correct visualization of the fact that one degree rise in temperature of x leads to two leads to two degree rise in temperature of y. This should be properly interpreted so one is prone to make mistakes in this.