Two thermometers $X$ and $Y$ have ice points marked at $15^{\circ}$ and $25^{\circ}$ and steam points marked as $75^{\circ}$ and $125^{\circ}$ respectively. When thermometer $X$ measures the temperature of a bath as $60^{\circ}$ on it,what would thermometer $Y$ read (in $^{\circ}C$) when it is used to measure the temperature of the same bath?

$A$ faulty thermometer has its fixed points marked $5^{\circ}$ and $95^{\circ}$. This thermometer reads the temperature of a body as $59^{\circ}$. Then the correct temperature of the body on the Celsius scale is ........ $^{\circ}$.

What is the difference between $^oC$ and $^oF$ thermometer values for freezing and boiling points of water?

The temperature of a substance increases by $27^{\circ}C$. On the Kelvin scale,this increase is equal to ........ $K$.

Answer the following:
$(a)$ The triple-point of water is a standard fixed point in modern thermometry. Why? What is wrong with taking the melting point of ice and the boiling point of water as standard fixed points (as was originally done in the Celsius scale)?
$(b)$ There were two fixed points in the original Celsius scale as mentioned above,which were assigned the numbers $0^{\circ}C$ and $100^{\circ}C$ respectively. On the absolute scale,one of the fixed points is the triple-point of water,which on the Kelvin absolute scale is assigned the number $273.16\; K$. What is the other fixed point on this (Kelvin) scale?
$(c)$ The absolute temperature (Kelvin scale) $T$ is related to the temperature $t_c$ on the Celsius scale by $t_c = T - 273.15$. Why do we have $273.15$ in this relation,and not $273.16$?
$(d)$ What is the temperature of the triple-point of water on an absolute scale whose unit interval size is equal to that of the Fahrenheit scale?

If the two temperatures on the Fahrenheit scale differ by $54^{\circ}\text{F}$, then the difference in temperature on the Celsius scale is (in $^{\circ}\text{C}$)