c - echo $PATH in system() give me a wrong output

This is a piece of code found on Internet

#include                                                                                                                                      
#include 



int main(int argc, char* argv[])
{
    putenv("PATH=/nothinghere");
    //setenv("PATH","/nothinghere");
    system(argv[1]);
    return 0;
}

if I do

$./a.out "ls"
sh: 1: ls: not found

Of course
But what if

$./a.out "echo $PATH"
/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/usr/games:/usr/local/games

It print the original $PATH !!

If we create a new shell then do the samethings

int main(int argc, char* argv[])
{

    putenv("PATH=/nothinghere");
    //setenv("PATH","/nothinghere");
    system("/bin/sh");
    return 0;
}

$./a.out
$ echo $PATH
/nothinghere
$ ls

/bin/sh: 2: ls: not found

Why?
Is it kind of problem about fork or the implementation of echo?

Answer

This is because you're using double quotes, telling your shell to replace $PATH with the value of the PATH variable before it even starts a.out.

The wrong value is thus being inserted not by the shell invoked by system(), but by the shell you're interactively typing commands at.

To fix it, change:

$ ./a.out "echo $PATH"

to:

$ ./a.out 'echo $PATH'