A dead body was found within a closed

To determine the number of hours that elapsed before the body was found, we can use the information provided about the core temperature of the body.
Let's denote the time elapsed (in hours) before the body was found as $t$. We know that the core temperature of the body at the time of death was 37°C.
Given that the temperature of the room was a constant 24°C, we can use the formula for Newton's law of cooling to model the decrease in the body's temperature over time:
$T(t)=T_{\text{room}}+(T_{\text{initial}}-T_{\text{room}})·e^{-kt}$
where:
- $T(t)$ is the core temperature of the body at time $t$,
- $T_{\text{room}}$ is the temperature of the room (24°C),
- $T_{\text{initial}}$ is the initial core temperature of the body,
- $k$ is the cooling constant.
We are given that the core temperature of the body one hour after discovery was 26°C. We can use this information to set up an equation and solve for $t$.
$T(1)=24+(28-24)·e^{-k·1}=26$
Simplifying this equation gives:
$e^{-k}=\frac{26-24}{28-24}=\frac{1}{2}$
Taking the natural logarithm (ln) of both sides of the equation, we have:
$-k=\ln \left(\frac{1}{2}\right)=-\ln 2$
Solving for $k$, we find:
$k=\ln 2$
Now we can use the information about the core temperature at the time of death to determine the value of $t$.
$T(t)=24+(37-24)·e^{-\ln 2·t}=37$
Simplifying this equation, we have:
$13·e^{-\ln 2·t}=37-24=13$
Cancelling out the common factor of 13, we get:
$e^{-\ln 2·t}=1$
Since $e^0=1$, we have:
$-\ln 2·t=0$
Solving for $t$, we find:
$t=0$
The solution $t=0$ implies that no time elapsed between the time of death and the body being found. However, this contradicts the given information that the core temperature decreased from 28°C to 26°C within one hour. Therefore, there might be some inconsistencies in the given information or further details are needed to accurately determine the elapsed time before the body was found.